For Otago, Jordan Sheed, Craig Cumming and Aaron Redmond all passed 50, and the remaining eight batsmen contributed 86 runs to the total in the first innings.
Shane Bond took three wickets in his first six overs in his first Test match for a year, and Sri Lanka were bowled out for 154 with only Tharanga and Chamara Kapugedera passing 20.
In reply, New Zealand trailed by 41 with six wickets in hand, but Daniel Vettori's half-century helped score 206 against a Muttiah Muralitharan-led bowling attack.
After the match Jayawardene expressed the Sri Lankan team's disappointment about the incident, saying it was contrary to the spirit of the game, but Fleming and McCullum were unrepentant.
Kumar Sangakkara and Chamara Silva put on a stand of 121 runs to lift the Sri Lankans to a score of 268 in their first innings after Jayawardene chose to bat.
The third day belonged to Sri Lanka once more, with Silva reaching 152 not out by the end of the innings, and Chaminda Vaas chipping in with a well made 47.